%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:35:38 AM UTC 2026
% Result : Unsatisfiable 0.64s 0.50s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 27 unt; 0 def)
% Number of atoms : 85 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 32 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 14 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_unordered_pair_axiom3_2,axiom,
unordered_pair(x,y) = null_class,
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
cnf(c_34,plain,
unordered_pair(x,y) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom3_2]) ).
cnf(c_35,plain,
null_class = unordered_pair(x,y),
inference(copy,[status(thm)],[c_34]) ).
fof(prove_corollary_to_unordered_pair_axiom3_1,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
cnf(c_36,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(clausify,[status(thm)],[prove_corollary_to_unordered_pair_axiom3_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_51,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_930,plain,
( intersection(A,regular(A)) = null_class
| A = unordered_pair(x,y) ),
inference(paramod,[status(thm)],[c_35,c_51]) ).
cnf(c_931,plain,
( intersection(A,regular(A)) = unordered_pair(x,y)
| A = unordered_pair(x,y) ),
inference(paramod,[status(thm)],[c_35,c_930]) ).
cnf(c_52,plain,
( intersection(A,regular(A)) = unordered_pair(x,y)
| unordered_pair(x,y) = A ),
inference(copy,[status(thm)],[c_931]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_99,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_100,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_102,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(cartesian_product2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( member(VAR_1,VAR_3)
| ~ member(ordered_pair(VAR_0,VAR_1),cross_product(VAR_2,VAR_3)) ),
file('theBenchmark.p',cartesian_product2) ).
cnf(c_108,plain,
( member(B,D)
| ~ member(ordered_pair(A,B),cross_product(C,D)) ),
inference(clausify,[status(thm)],[cartesian_product2]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_110,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_111,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_110]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_112,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_113,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_112]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_115,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_119,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_121,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_124,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_187,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_100]) ).
cnf(c_932,plain,
( member(B,D)
| ~ member(unordered_pair(singleton(A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_111,c_108]) ).
cnf(c_933,plain,
( member(B,D)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,singleton(B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_113,c_932]) ).
cnf(c_190,plain,
( member(B,D)
| ~ member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(C,D)) ),
inference(paramod,[status(thm)],[c_113,c_933]) ).
cnf(c_934,plain,
member(unordered_pair(singleton(x),unordered_pair(x,singleton(y))),cross_product(u,v)),
inference(paramod,[status(thm)],[c_111,c_36]) ).
cnf(c_935,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,singleton(y))),cross_product(u,v)),
inference(paramod,[status(thm)],[c_113,c_934]) ).
cnf(c_199,plain,
member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(u,v)),
inference(paramod,[status(thm)],[c_113,c_935]) ).
cnf(c_246,plain,
subclass(A,A),
inference(xxres,[status(thm)],[c_119]) ).
cnf(c_251,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_124,c_121]) ).
cnf(c_330,plain,
member(y,v),
inference(resolve,[status(thm)],[c_199,c_190]) ).
cnf(c_368,plain,
member(y,intersection(v,v)),
inference(resolve,[status(thm)],[c_330,c_187]) ).
cnf(c_371,plain,
~ member(y,complement(v)),
inference(resolve,[status(thm)],[c_99,c_330]) ).
cnf(c_400,plain,
~ member(y,intersection(complement(v),A)),
inference(resolve,[status(thm)],[c_102,c_371]) ).
cnf(c_465,plain,
member(y,universal_class),
inference(resolve,[status(thm)],[c_251,c_368]) ).
cnf(c_495,plain,
member(y,unordered_pair(A,y)),
inference(resolve,[status(thm)],[c_465,c_115]) ).
cnf(c_936,plain,
( member(y,B)
| ~ subclass(unordered_pair(A,y),B) ),
inference(resolve,[status(thm)],[c_124,c_495]) ).
cnf(c_607,plain,
~ subclass(unordered_pair(A,y),complement(v)),
inference(resolve,[status(thm)],[c_936,c_371]) ).
cnf(c_937,plain,
( ~ member(y,unordered_pair(x,y))
| unordered_pair(x,y) = complement(v) ),
inference(paramod,[status(thm)],[c_52,c_400]) ).
cnf(c_938,plain,
( ~ member(y,unordered_pair(x,y))
| complement(v) = unordered_pair(x,y) ),
inference(copy,[status(thm)],[c_937]) ).
cnf(c_871,plain,
complement(v) = unordered_pair(x,y),
inference(resolve,[status(thm)],[c_495,c_938]) ).
cnf(c_928,plain,
~ subclass(unordered_pair(A,y),unordered_pair(x,y)),
inference(paramod,[status(thm)],[c_871,c_607]) ).
cnf(c_929,plain,
$false,
inference(resolve,[status(thm)],[c_928,c_246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET075-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:06:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1080087 was started by sandbox2 on n002,
% 0.13/0.36 % Sat Sep 26 07:06:20 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.64/0.50
% 0.64/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.64/0.50
% 0.64/0.50 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.64/0.50 % Length of proof is 32.
% 0.64/0.50 % Level of proof is 9.
% 0.64/0.50 % Maximum clause weight is 16.000.
% 0.64/0.50 % Given clauses 173.
% 0.64/0.50
% 0.64/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------